Some natural equivalence relations in the Solovay model

Abstract

We obtain some non-reducibility results concerning some natural equivalence relations on reals in the Solovay model. The proofs use the existence of reals x which are minimal with respect to the cardinals in L[x], in a certain sense.

Keywords

Equivalence relations Solovay model Forcing Constructibility

Communicated by B. Löwe.

S.-D. Friedman research was supported by Grant P 19375-N18 of the Austrian Science Fund (FWF).

V. Kanovei research was supported by Grants 06-01-00608 and 07-01-00445 of the Russian Foundation for Basic Research (RFBR).